Electronic devices with a rechargeable energy storage and with means for a wireless communication are known in a large variety of designs and for many different applications, for example as mobile computing devices, mobile phones, game consoles, remote controls etc. Important examples of such devices are also found in medical applications, for instance as implantable devices like the one described in the U.S. Pat. No. 6,894,456 B2, which is concerned with an implantable power module with means for inductive charging of a battery. Moreover, said power module comprises means for a remote communication via e.g. radiofrequency (RF). In this and similar devices, the radio communication means are always active, at least in a standby mode, which is associated with a continuous power consumption. Continuous power consumption by an RF-unit on stand-by is problematic in rechargeable implantable medical devices since the available energy is limited and the battery can only be recharged a limited number of times.